Field Assisted Sintering Technique Courtesy of Prof. Ricardo Castro (rhrcastro@ucdavis.edu) and Dr.

D. V. Quach (dvquach@ucdavis.edu)

Early Sintering Stage

Sintering Driving Forces

Why Sintering Happens?

1) Surface Energy

Blow

Here STOP

When you blow a film of soap, an arc will form while you’re blowing.

When you stop, the surface becomes flat.

This is because there is an extra energy to create a surface.

In this case, it is a reversible work (provided by blowing) needed

increase the surface of a unit area.

dA

dwR

Surface tension is different however

from surface enery.

Surface energy is the energy

needed to create a new surface and

not only tension it to expand.

In liquids, there is no difference

between them, but in solids, they

are usually different. This is

because to create a surface in a

solid means to create a surface free

of tension and in equilibrium. If this

surface is ever tensioned, this

tension will remain, since the

atomic mobility is very limited.

inPT

SdA

dE

,,

The surface energy will always drive the small particles to be

unstable. The system tends to decrease its energy even if locally,

for instance by defining new shapes proportional to the interface

energies.

Wulff’s figure

Example: Determine the equilibrium

shape of the grain below using Wulff’s

principle and knowing that: (110) = 2

erg/cm2; (121) = 1.5 erg/cm2; (111) =

0.5 erg/cm2; (101) = 4 erg/cm2:

AAdAdG

The driving force related to the interface energy is:

Two phenomena that occur during sintering:

Densification + Coarsening

The system is eliminating one surface but creating another.

But surface energy is not the only driving force acting during

sintering, and LOCAL driving forces apply.

2) Pressure due to curvature

If you blow a straw inside oil,

you’re providing work

needed to expand the

spherical surface. This work

(pressure . volume) must be

equal to the area variation

times the surface tension

( .dA).

dAPdV

If the area is spherical, the volume variation is dV=4 r2dr, and

the variation of area is dA=8 rdr, where r is the radius,

then:

rdrr

rdr

dV

dAP

2

4

8

2

The smaller the radius, the higher the pressure needed to

create it, and vice-versa.

infinite

Chemical potential is related to vapor pressure (or

solubility) by:

pRT ln

0lnln pRTpRT

rdrdAp

pRT 8ln

0

rRT

Vpp

M 2exp

0

24 r

Vdr

M

The difference of the chemical potential for an atom in

the curved surface (p) and in a flat surface (p0) will be

given by the curvature only.

If dV=4 r2dr,

3) Vapor Pressure Difference

G

G

rG

XrXX

BX

G

r1 r2

Concentration

Since the solubility (or vapor pressure) is

dependent on the particle size (because of

curvature), we expect the small particles to

dissolve/evaporate and re-precipitate (condense)

on the larger ones.

dA

dwR

dA

dwR

dA

dwR

In Sintering:

Moving material from the convex

surface to the concave surface

of the pore. Evaporation- at flat

or convex surfaces,

condensation – at concave

surfaces.

Other Driving

forces:

Vacancy Conc. can

be considered a

dispersed phase in

vacuum

Stages of

Sintering

1 2

3 4

http://www.esrf.eu/UsersAndScience/Publications/Highlights/2002/Materials/MAT3

Driving Forces during

Initial Stage of Sintering

Two particles model

The pressure difference is given by

If:

The vapor pressure difference is given by:

The vacancy concentration difference is:

dV

dAP

AAdAdG

Material transport mechanism during sintering

Material transport paths during sintering

x – neck size

a- particle radius

Summary of kinetic equations for various mechanisms of initial

stage sintering

Current/Field Role in Sintering

Field/current in conductive and non-conductive

materials

Same sintering stages? Mechanisms? Materials

dependence?

Evaporation

Plasma - difficult to capture experimentally (setups

precluding plasma generation)

Dielectric induced plasma generation in flash

sintering

Local fields

Field contribution to early sintering (e. g., polarization

effects)

Stage 1 – enhanced kinetics

Early Sintering Stage (FAST) Initial sintering stage-usually when x= 2/3 a. Olevsky: transition point based upon the kinetics of the various mass transfer mechanisms • Undoped Y2O3 30 nm – onset at 873 vs 1473 in CS (Yoshida et al, 2008) • SnO2 - 92% TD in 10 min at 1163 K vs CS: 61% TD in 3 h at 1273 K (Scarlat et al, 2003)

• Enhanced densification in Al2O3 (Stanciu et al, J.Am.Ceram.Soc. 2007)

Arrhenius plot of (αρ) for nano α-

Al2O3 sintered by different techniques:

α – thermal diffusivity

ρ – density

The product (αρ) is proportional to the

relative neck radius.

• Maximum shrinkage rates 1-2 order of magnitude higher than CS (973 K for ZnO, 1373 K for ZrO2 and 1423 K for Al2O3) (Nygren and Shen, 2003).

FAST sintering curves for ZnO, 3YSZ and Al2O3 with a heating rate of 100 oC.min-1

Clean grain boundaries in

metals and ceramics

“Cleaning” Effects

TEM of FAST sintered AlN

Cu sphere-plate experiments under current application (900 oC) Multilayer graphite / copper plungers to control current density at constant power (P=I2R) Frei J M, Anselmi-Tamburini U and Munir Z A (2007), ‘Current effects on neck growth in the sintering of copper spheres to copper plates by the pulsed electric current method’, J. Appl. Phys., 101, 114914/1-8.

Enhanced Neck Growth

]24)1(22[2

sagfcocucpRxRxRRxRIP

2/1

2/124

1

gfcoRR

P

xI

Effect of current on neck formation between copper spheres and copper plates at

900 oC for 60 min: (a) no current, (b) 700 A, (c) 850 A, and (d) 1040 A

Enhanced Neck Growth – cont’d

Conventional (no current) sintering: n = 4.13 (volume diffusion with E-C contribution) Different sintering mechanisms under current application: n = 8.76 – 20.64 (different sintering mechanisms than in CS) Evaporation-condensation (E-C), surface diffusion (SD) contributions to re-start neck growth (by faster coarsening step) E-C, SD visualized as new ledge patterns around the necks and voids, depending on current magnitude (no ledges in CS). Cu vapor pressure at 900 C: 10-4 Pa (insufficient for significant mass transport) Enhanced evaporation by adatom detachment form ledges or desorption from terraces due to electromigration force (F = Z*eE) Voids at the neck edge:

Evaporation-Condensation vs Surface

Diffusion

• Demonstrated enhanced evaporation

• Enhanced grain boundary and volume diffusion

• Surface diffusion – no effect due to external current in

YSZ (70 nm)

Neck formation (n, Q values by ionic conductivity

measurements) – in early stages with negligible

shrinkage.

σt (σi)= sample (intrinsic) conductivity (with Q=Qi+Q/n),

Xt= diameter of contact area

M. Cologna, R. Raj, Surface Diffusion-Controlled Neck Growth Kinetics in Early

Sintering of Zirconia with or without Applied DC Electrical Field, JACS, 2010,

1-5

)(2 d

Xti

t

MOLECULAR DYNAMIC SIMULATIONS

Results with no field applied and pulses of 109V/m applied of 1, 5, 10, and 50 ps

duration (on /off). displacement of surface and bulk atoms in an AlN nanosphere

of 4 nm radius (25,384 atoms).

Plasma, Sparks, Breakdown

No plasma under specific FAST conditions (>100 C, no local

effects)

Arc discharges → electron emissions

Dielectric breakdown: intrinsic or soft

Electric field enhancement – local field effects (e. g.,

about 200x in HA)

Dielectric induced plasma generation in flash sintering

Enthalpy (bonding) (ΔH0) changes in dielectrics:

po- dipole moment, k- dielectric constant, E- electrical field

(McPherson, J et al, APL, 82, 2121, 2003)

Ek

pHHo

)3

2(

0

Spark (Electric

Arc)

Visual observation

-effect of pulsed current on neck

formation during the sintering of

550 um Cu powder in a custom-

designed FAST equipment

(optical microscope).

Yanagisawa O, Kuramoto H, Matsugi K, Komatsu

M (2003), ‘Observation of particle behavior in

copper powder compact during pulsed electric

discharge’, Mat Sci Eng A, 350, 184-189.

Spark (Electric Arc) –

Contd.

Visual observation

-Local melting was also observed at

locations where strong sparks occurred

- A minimum macroscopic current density

for spark to occur (e. g., 10 kA cm-2 at 6.9

MPa pressure)

-Current density - two orders of magnitude

greater than in a typical FAST

- Local current density at particle contact

can be higher.

- Spark formation at lower pressure and

higher current density

- Spark probability at particle contacts is

low (less than 2% in the above work).

Pulsing Current Effects

PAS sintering of ~3 μm Cu powders.

Initial Pulsed Current : 30 s – 80 ms on/80 ms off

Temp measurements – thermocouple inside the powder bed

Pulsed current promoted an earlier onset of sintering (compared to direct current).

Time of maximum shrinkage displacement (t msd) was 180 s under pulsed current

vs 240 s with no pulses (at 420 A).

No pulsing effect at > 700 A

Xie et al (2003) found no effect of pulsing on final density, electrical resistivity and

mechanical properties of fully sintered Al. It is possible that the magnitude of the pulsed

current overshadows any influence of the pulse pattern. Wang S W, Chen L D, Kang Y S, Niino M, Hirai T, (2000), ‘Effect of plasma activated sintering (PAS)

parameters on densification of copper powder’, Mater. Res. Bull., 35, 619-628.

Xie G, Ohashi O, Chiba K, Yamaguchi N, Song M, Furuya K and Noda T (2003), ‘Frequency effect on pulse

electric current sintering process of pure aluminum powder’, Mat Sci Eng A, 359, 384-390

Pore Stability

The surface curvature of the grains around an isolated

pore is affected by their number and the dihedral

angle.

Three possible mechanisms for pore motion: surface

diffusion, volume diffusion through the vapor phase, and

volume diffusion through the matrix.

Does evaporation control pore elimination in late sintering

stages?

Raichenko argument

Final Sintering Stages (Raichenko)

Higher electric current density at the root of large pores (R-pore radius) creates temperature gradients which in turn produce a vacancy gradient and mass transport in opposite sense ( o - electrical conductivity, CM - specific heat, To- initial temperature, Eo- intensity of electric field, - time of electric field effect):

n

ET

CRT

M

2

000

2

1

Conclusion: large pores shrink under applied electric current.

The velocity of the migration of a pore is defined by both mobility and force:

Pore Elimination

Bibliography

S-J. L. Kang; Sintering: Densification, Grain Growth &

Microstructure, Elsevier 2005

Others: R. W. Baluffi et al.; Kinetics of Materials, Wiley 2005

R. M. German; Sintering Theory and Practice, Wiley 1966

M. N., Rahaman; Ceramic Processing and Sintering, 2nd Ed., CRC Press,

2003

D. A. Porter et al.; Phase Transformations in Metals and Alloys, CRC Press,

2008

Y.-M. Chiang et al.; Physical Ceramics - Principles for Ceramic Science and

Engineering, John Wiley & Sibs Inc. 1997